A number of removable dental appliances, mouthpiece devices, and similar medical devices have been developed to assist patients with a wide variety of ailments including bite correction, snoring, sleep apnea, bruxism, and tooth loss. Removable dental appliances can include teeth aligners, dentures, retainers, bruxism guards, night guards, snoring mouthpieces, athletic mouthguards, and other devices. Given that these devices are often placed directly in the user's mouth, such devices can be sensitive to contamination, as germs, bacteria, and viral agents can be transferred from the appliance to the user's mouth and vice versa. Further, dental appliances, like many medical devices, can be custom-designed and individually-prescribed by medical and dental health professionals. In some cases, these appliances can be quite expensive. Accordingly, many removable appliances are provided together with a carrier to safeguard the appliance while it is not in use. A common appliance carrier can take the form of a rigid plastic case adapted to enclose the appliance while protecting the appliance from falls or impact trauma. Other medical devices and tools can also be sensitive to contamination and can be provided with specialized containers to protect the devices from contamination and contact while not in use.